Multivariate and functional classification using depth and distance

Multivariate and functional classification using depth and distance We construct classifiers for multivariate and functional data. Our approach is based on a kind of distance between data points and classes. The distance measure needs to be robust to outliers and invariant to linear transformations of the data. For this purpose we can use the bagdistance which is based on halfspace depth. It satisfies most of the properties of a norm but is able to reflect asymmetry when the class is skewed. Alternatively we can compute a measure of outlyingness based on the skew-adjusted projection depth. In either case we propose the DistSpace transform which maps each data point to the vector of its distances to all classes, followed by k-nearest neighbor (kNN) classification of the transformed data points. This combines invariance and robustness with the simplicity and wide applicability of kNN. The proposal is compared with other methods in experiments with real and simulated data. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Data Analysis and Classification Springer Journals

Multivariate and functional classification using depth and distance

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Statistics; Statistical Theory and Methods; Data Mining and Knowledge Discovery
ISSN
1862-5347
eISSN
1862-5355
D.O.I.
10.1007/s11634-016-0269-3
Publisher site
See Article on Publisher Site

Abstract

We construct classifiers for multivariate and functional data. Our approach is based on a kind of distance between data points and classes. The distance measure needs to be robust to outliers and invariant to linear transformations of the data. For this purpose we can use the bagdistance which is based on halfspace depth. It satisfies most of the properties of a norm but is able to reflect asymmetry when the class is skewed. Alternatively we can compute a measure of outlyingness based on the skew-adjusted projection depth. In either case we propose the DistSpace transform which maps each data point to the vector of its distances to all classes, followed by k-nearest neighbor (kNN) classification of the transformed data points. This combines invariance and robustness with the simplicity and wide applicability of kNN. The proposal is compared with other methods in experiments with real and simulated data.

Journal

Advances in Data Analysis and ClassificationSpringer Journals

Published: Aug 17, 2016

References

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